Talk:2017 Spring Event/@comment-31639004-20170331154649
I've been math-ing about a bit, and it seems that Bronze Chests are actually pretty good at getting you Daily Specials. Check this out: Bronze costs 40 lanterns; it grants 70 lanterns 20% of the time (expect 14 lanterns per chest; net 26 lanterns). Silver costs 70 lanterns; it grants 120 lanterns 15% of the time (expect 18 lanterns per chest, net 52 lanterns). Gold costs 120 lanterns; it grants 200 lanterns 12% of the time (expect 24 lanterns per chest, net 96 lanterns). Right away, Bronze Chests look a bit more reasonable. If we score the lanterns award, we'll just spend it again anyway, right? This being the case, we can normalize reward percentages to exclude the lantern rewards. That is, with the 20% lantern award factored out, all other Bronze Chest prizes are 1.25 (that is, 100% / (100% - 20%) ) times more likely. These factors work out as follows for the Daily Specials: Bronze 7% Daily x 1.25 factor = 8.75% Silver 13% Daily x 1.18 factor = 15.29% Gold 25% Daily x 1.14 factor = 28.41% Doing this will also mean adjusting the blossom rewards, since re-rolling comes with extra blossoms. Even in a math-heavy post, I need to apologize -- this gets especially ugly. Generic formula: T = B + (T)(P)(L/C); therefore T = B / (1-PL/C) T: Total Blossoms B: Blossoms awarded for opening a single chest P: Probability of winning lanterns L: Lanterns awarded C: Lanterns cost to open chest Bronze '''has adjusted Blossoms of 5 / (1 - (0.2)(70) / 40) = 7.69 '''Silver '''has adjusted Blossoms of 10 / (1 - (0.15)(120) / 70) = 13.46 '''Gold '''has adjusted Blossoms of 20 / (1 - (0.12)(200) / 120) = 25.00 How well does a lantern return a Daily for each chest? '''Bronze 8.75% / 26 lanterns = 0.337% per lantern Silver 15.29% / 52 lanterns = 0.294% per lantern Gold 28.41% / 96 lanterns = 0.296% per lantern What about the Grand Prize? Bronze 7.69 blossoms / 26 lanterns = 0.296 blossoms / lantern Silver 13.46 blossoms / 52 lanterns = 0.259 blossoms / lantern Gold 25 blossoms / 96 lanterns = 0.260 blossoms / lantern So, if you're working toward the Grand Prizes, Bronze Chests are slightly better. Here's the thing, though. The Grand Prize is awarded for large, discreet chunks of 120 blossoms. It takes a lot of these chunks for the extra 13.67% blossoms to add up. Elsewhere, I've come up with an estimate of 1358 lanterns for the event. Using Bronze will net you about 402 lanterns - enough to easily score the first two Grand Prizes, but not quite enough for the third. Not included in these calculations is the extra tree that spawns when you open a chest. Experimentally, I got a single tree when opening a Gold Chest. Does this happen every time a Gold Chest is opened? What about a Bronze Chest? If both spawn a single tree, Bronze Chests win both Daily Special and Grand Prize due to the impact the tree will have on the lower cost. I want to learn more about these trees! Lastly, many of the prizes for Bronze Chests are pretty lackluster. Unattached units don't really thrill the way a new building does. Forge Point awards would favor Bronze Chests due to higher percentage of award. Other awards will depend on player preferences. TL/DR; If you really want a certain Daily Special, save up your lanterns and use them on Bronze Chests!